Question

The simplified from of (-1)³×(-1)⁶ is ___________
a) -1
b) 1
c) (-1)¹⁸
​

Answer 1

Hello buddy... Your answer is option (a)-1

Step-by-step explanation:

(-1)³×(-1)⁶

=(-1)×(1)

=(-1)

Note: When the power of a negative number is odd , your answer also would be negative & on the other hand , if the power is even the answer would be positive.

eg 1 : (-1)⁷

Here , the power, 7 is odd . So the answer would be negative.

That is (-1) itself.

eg 2 : (-1)⁴

Here , the power 4 is even . So your answer would be positive .

That is (+1).

Hope this helps you !

Answer 2

Given :   (-1)³×(-1)⁶

To Find : simplified form

a) -1

b) 1

c) (-1)¹⁸

Solution:

Law of exponents:

${{\text{a}}^{n}}\times {{a}^{-n}}=1\text{ or }{{\text{a}}^{n}}=\frac{1}{{{a}^{n}}} \\ & {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \\ & \frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}} \\ & {{\left( {{a}^{m}} \right)}^{n}}={{\left( {{a}^{n}} \right)}^{m}}={{a}^{mn}} \\ & {{a}^{m}}\times {{b}^{m}}={{\left( ab \right)}^{m}} \\ & \frac{{{a}^{n}}}{{{b}^{n}}}={{\left( \frac{a}{b} \right)}^{n}} \\ & {{a}^{0}}=1$

(-1)³×(-1)⁶

= (-1)³⁺⁶

= (-1)⁹

= (-1)¹⁺⁸

= (-1)¹ * (-1)⁸

= -1 * ((-1)²)⁴

(-1)² = 1

= - 1 * (1)⁴

= - 1 * 1

= - 1

Hence simplified form of  (-1)³×(-1)⁶ is -1

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